Methane Reforming Demonstration Problem
Contents
1. plus a trace H2 CO Extra steam reactor 1100 an set flows Discretized Reactor reactor 1 reactor 2 reactor reactor 4 ctor 5J reactor 63 reactor 7 eactor 8 4 reactor reactor 1 reactor 1001 i 3 Pipe reactor 1 gt Sep Ser Se Ser a S S R Srens Sra The corresponding FloCAD diagram is as follows p gt ABP b gt a p gt fit gt t ptf 66 Tanks must be used within the Pipe to allow species source sink rates XMDOTs to be specified reactions are not possible in junctions Note that STUBE connectors inertia less duct elements are used instead of tubes since the flows consist of low density gases Even though the subsequent transient operates over an extremely short time scale tubes would not be required unless significant condensation were to occur The STDSTL solution must be used to arrive at a steady state answer since chemical reactions are not possible in STEADY which treats tanks as if they were junctions Normally a STEADY steady state solution is not very dependent on initial conditions and often only requires 10 50 iterations to resolve However an STDSTL solution uses the full transient hydrodynamic solution along with a simultaneous The restart record number integer register record will also have to be adjusted based on the outputs of the first case pfr since the size of the SAVE and RSI RSO files will change if the model size changes S Assuming te2. For example preliminary CEA runs could have generated equilibrium state predictions perhaps as functions of temperature which could have been used as inputs to the EQRATE utility If instead only the rate of reaction is known as is the case in this example then EQRATE is not applicable and the XMDOT values should instead be calculated explicitly by the user in user logic block FLOGIC 0 at the start of each solution interval i e time step or steady state relaxation step The XMDOT value for each species i will be the sum of all the reactions in which it participates The resulting set of XMDOT values is assumed to be constant along with the corresponding QCHEM over the next solution interval In other words the species production and extinction rates are based on the temperatures and pressures at the start of the interval and are not implicitly adjusted for temperature or pressure changes that are about to occur A significant restriction on chemical reactions is that they can only apply to tanks control volumes and not to junctions massless volumeless state points Noting that the main solution routine STEADY aka FASTIC treats tanks temporarily as junctions this means that steady state solutions can only be achieved using STDSTL pseudo transient integration toward a time independent state This in turn means that unlike most steady state analyses chemical reaction steady state solutions are dependent on initial gu
3. Stoichiometric equal mole and other inlet stream mol_in_w 0 5 fractions plus 2 times more constituents plus excess steam SteamX 3 0 steam Use SteamX 1 0 for fraction beyond stoichiometric stoichiometric feed rates Outlet pressure pres 101325 Pa This indirectly sets the reactor pressure due to the small pressure drop through the reactor A Refresher Modeling Reactions in SINDA FLUINT The rate of creation of mass of any species i is designated XMDOTi in SINDA FLUINT with the caveat that XMDOTi 0 there is no net generation or loss of total mass as a result of a chemical reaction A species that is being consumed will have a negative XMDOT and a species that is being produced will have a positive XMDOT Since this model uses metric units XMDOT has units of kg s lb hr would be the units in the English system When XMDOTSs are nonzero the code will automatically calculate and apply a corrective heat of reaction QCHEM based on the fluid properties heats of formation and enthalpy basis If each fluid uses the heat of formation as the enthalpy basis at STP this corrective QCHEM term is zero When the desired concentration of one or more species is known e g when either the equilibrium concentration or the reaction combustion efficiency is known the EQRATE utility can be used to generate XMDOT values perhaps obeying one or more chemical reactions supplied as stoichiometric numbers
4. Therefore properties for all five gases were generated using NASA s free CEA chemical equilibrium program combined with a C amp R utility for converting outputs to FPROP DATA format While this interface is intended to prepare fluids representing equilibrium reacting mixtures with variable molecular weights the only mode in CEA can be used to produce properties for single constituents with constant molecular weights Therefore despite the resulting generalized 6000 series real gas fluid tables it should be noted that the actual properties reflect CEA s intrinsic assumption of perfect gases Heat of formation HFORM and diffusion volume DIFV information were then added to these fluid files noting that CEA uses the heat of formation as the basis of the enthalpy at 25 C The heat of formation of water is therefore diminished by the heat of vaporization to reflect the all gas nature of this CEA derived fluid file For a full two phase water description the uncorrected heat of formation should instead be applied since a liquid state exists at standard temperature and pressure Reactor Design An intentionally generic and simplified plug flow reactor PFR is assumed Inclusion of the solid catalyst particles could take several forms as a packed bed of stationary particles held in place by structured catalysts supports free flowing with the gas transport or other configurations but inclusion of the catalysts in any form ov
5. 0 c reaction 2 c mol kg Pa s klc2 c unitless 12 9 EXP 8074 3 atemp Kuc2 EXP 44 00 0 atemp 4 063 rxn2 klc2 ppgg thisppgw this ppgh this amp ppgc this Kuc 2 apres DEN 2 rate2 rxn2 dl this vol this rate2 xmdotg this xmdotw this xmdotc this xmdoth this c store key data away damping 1 0 rateLag rate2 rateLag cy this xmdotg this rate2 mw_co xmdotw this rate2 mw_h2o xmdotc this rate2 mw_co2 xmdoth this rate2 mw_h2 in otherwise unused CX CY CZ cells for ease of postprocessing cx this ratel cy this rate2 c a little out of step uses last QCHEM and QCHEM is for both reactions c but if ratel ne 0 0 cz this 1 e 6 qchem this ratel The above is the basis of the Sinaps model pfr_nl smdl and the FloCAD model pfr_nl dwg where the nl in the names refers to the Network Logic option The difference to the two approaches is largely a matter of user preference Network logic is expanded translated by Sinaps or FloCAD and inserted into the specified location FLOGIC 0 in this case Note that the key difference is how to reference each property di lump in HEADER SUBROUTINES where lump has been calculated using the dynamic translation function INTLMP is equivalent to dl this in network logic opg methane lump in HEADER SUBROUTINES where methane is an integer calculated using the dynamic functi
6. a warming of the middle of the reactor and therefore more complete reforming of the inflowing methane Transient Response to Steam Reduction reactor TL1 reactor TL2 reactor TL3 reactor TL4 reactor TL5 reactor TL6 reactor TL7 reactor TL8 reactor TL9 reactor TL10 Temperature C 0 0 02 004 O06 0 08 0 1 0 12 0 14 O16 0 18 0 24 Time sec An alternative view of this same event is depicted below in terms of the partial pressure fraction mole fraction of hydrogen gas As the excess steam is withdrawn the fraction of hydrogen jumps first at the inlet and this front can be seen progressing through the reactor for the first 0 16 seconds The reactor shifts from producing 55 H2 to more optimum 72 the maximum possible is 75 Transient Response of Partial Pressure Mole Fraction of H2 to Steam Reduction a r ZA reactor PPGH1 reactor PPGH2 reactor PPGH3 reactor PPGH4 reactor PPGH5 reactor PPGH6 reactor PPGH7 reactor PPGH8 reactor PPGH9 reactor PPGH10 Partial Pressure Mole Fraction of H2 0 0 02 0 04 0 06 0 08 0 1 0 12 0 14 0 16 0 18 0 2 0 22 0 24 Time sec Validation with Aspen Plus Like NASA s CEA AspenTech s Aspen Plus can be used to predict equilibrium constituent frac
7. feed ratios are not altered during the course of an analysis To demonstrate this modeling approach a variation of the above model was made and is available in Sinaps form First CEA was run for a stoichiometric mixture of water and methane restricting the resulting mixture to only the five species used in the original analysis i e excluding carbon other minor species ions etc This table of CEA equilibrium data was converted into a single SINDA FLUINT FPROP block using the cea2fprop utility and the heat of formation was set to be the same as the enthalpy of this new fluid at STP This new fluid was then used in the PFR model as species E such that when M methane and W water are reacted they result in this variable weight equilibrium fluid as follows CH H20 amp E equivalent reaction The species H hydrogen G carbon monoxide and C carbon dioxide are therefore eliminated from the model Note that methane and water constitute significant portions of fluid E especially below 600 C By assuming equilibrium the kinetic rate calculations are eliminated In fact reactions in all but the first tank are eliminated as well downstream reactions are taken care of by temperature and pressure dependent shifts within the equilibrium fluid itself While the utility EQRATE could have been used to set XMDOT values instead the reaction rates in the first tank tank 1 were set in FLOGIC 0 applying a reactio
8. liquid at STP could be included The results of this validation exercise are summarized below Six diabatic cases were compared three with both feed and products at the same temperature 500 C 800 C and 1000 C and three with feed at 25 C while product temperatures remained the same The predicted species mole fractions are tabulated below along with the two power rates Qr for T Tp and Qs for T 25 C The differences are expressed as percentages which are calculated based on total mass for species fractions 500 C 800 C 1000 C Aspen S F diff Aspen S F diff Aspen S F diff cH _ 0 3203 0 3188 0 14 0 0269 0 0262 0 07 0 0009 0 0009 0 00 H20 0 2493 0 2475 0 18 0 0199 0 0196 0 03 0 0008 0 0008 0 00 co 0 0189 0 0193 0 04 0 2296 0 2304 0 07 0 2495 0 2495 0 00 CO 0 0710 0 0713 0 03 0 0069 0 0066 0 04 0 0001 0 0001 0 00 H2 0 3406 0 3431 0 25 0 7166 0 7173 0 06 0 7488 0 7487 0 00 Qp kJ mol 126 99 128 13 0 89 319 45 318 64 0 26 393 94 393 49 0 11 Qos kJ mol 42 18 42 70 1 22 201 77 202 14 0 19 225 40 224 58 0 36 Note that the agreement improves as the temperature rises faster reaction rates making equilibrium a more likely result but is very good even for the 500 C case considering that the two programs do not use the same approach the Aspen data assumes equilibrium and this particular SINDA FL
9. state approach Steady State Results With 3 times as much steam as needed for stoichiometric conditions SteamX 3 and given a feed temperature of 800 C and wall temperatures of 800 C as well the resulting temperature gradients at steady state are shown below Stoich Methane Water plus a trace H2 CO Extra steam gt gt Op O O amp S82 9 O7 Oy A Spy Sy Se 2p S SH SD DH SS DH SH 3 DS DS set flows Discretized Reactor wall A Set Sat Seb Sei Sei In the diagram above the fluid species are mixed in junction reactor 1001 without reactions yet permitted then injected at the left of the diagram exiting at the right The temperatures drop to about 550 C at the inlet before rising to about 780 C at the outlet If a longer reactor had been used the exit temperatures would have been closer to the wall temperature of 800 C If finer spatial resolution had been used for example 20 segments instead of 10 the results would have revealed that the coldest spot in the reactor is not exactly at the inlet but is instead located a few centimeters downstream where endothermic reaction 1 reaches its peak rate The corresponding partial pressure fraction mole fraction for hydrogen is shown next checker would still prevent convergence from being declared at the end of the run since it also checks the absolute size of the pseudo time step as an indication of a having achieved a time i
10. this limitation a separate CEA run could be made using the SINDA FLUINT predicted temperatures and pressures to calculate the fractional constituents of the equilibrium fluid at one or more points When used with appropriate cautions validating assumptions as needed the equilibrium fluid method can be a powerful companion approach to perform preliminary sizing and sensitivity analyses for example If kinetic rates are not known it might be the only approach available for first order estimations and bracketing analyses 1 Future plans call for the inclusion of all CEA capabilities within SINDA FLUINT which would eliminate this additional post simulation step Side Note Carbon coke Formation At one bar pressure with equal molar inputs of methane and steam stoichiometric conditions CEA predicts the following mole fractions versus temperature in degrees C As is evidenced by the above equilibrium Gibb s free energy minimization analysis the fraction of carbon coke graphite peaks at about 600 C at which point there are more moles of carbon in the mixture than either CO or CO While the presence of carbon has been neglected in this demonstration case it clearly must be included for a more complete treatment Therefore this section provides brief notes on how such a more detailed model could be constructed To include carbon in the methane reforming model another species must be int
11. G h2 lump KCO PPG co lump amp KH20 PPG water lump PPG h2 lump c reaction 1 c mol sqrt Pa kg s klel 8 336e17 EXP 28879 atemp c Pa 2 Kucl 10266 76e6 EXP 26830 atemp 30 11 rxnl klcl ppg methane lump ppg water lump ppg h2 lump 2 5 amp apres 2 ppg co lump sqrt ppg h2 lump Kuc1 amp sqrt apres DEN 2 ratel rxnl dl lump vol lump ratel 1 0 rateLag ratel rateLag cx lump xmdot methane lump ratel mw_ch4 xmdot water lump ratel mw_h2o xmdot co lump ratel mw_co xmdot h2 lump 3 0 ratel mw_h2 xmdot co2 lump 0 0 c reaction 2 c mol kg Pa s klc2 12 19 EXP 8074 3 atemp c unitless Kuc2 EXP 4400 0 atemp 4 063 rxn2 klc2 ppg co lump ppg water lump ppg h2 lump amp ppg co2 lump Kuc2 apres DEN 2 rate2 rxn2 dl1 lump vol lump rate2 1 0 rateLag rate2 rateLag cy lump xmdot co lump xmdot co lump rate2 mw_co xmdot water lump xmdot water lump rate2 mw_h2o xmdot co2 lump xmdot co2 lump rate2 mw_co2 xmdot h2 lump xmdot h2 lump rate2 mw_h2 c store key data away in otherwise unused CX CY CZ cells c for ease of postprocessing damping cx lump ratel cy lump rate2 c a little out of step uses last QCHEM and QCHEM is for both reactions c but if ratel ne 0 0 cz lump 1 e 6 qchem lump ratel
12. Methane Reforming Demonstration Problem Revision 0 October 14 2008 Reference Wang Shuyan et al Simulation of effect of catalytic particle clustering on methane steam reforming in a circulating fluidized bed reformer Chemical Engineering Journal 139 2008 136 146 Purpose and Overview Steam reforming of methane conversion of CH into syngas CO and H2 is of interest for applications such as fuel cells conversion of natural gas to liquid fuels etc Similar reactors are of interest for coal to liquid CTL and biofuel synthesis applications A simple demonstration problem has been developed in SINDA FLUINT using both the Sinaps nongeometric sketchpad GUI and the Thermal Desktop with FloCAD geometric CAD based GUI Since both sets of models are available for inspection and for use as a starting point or template only brief descriptions are included in this document as general guidance A basic understanding of SINDA FLUINT modeling is assumed Reaction Kinetics Two simultaneous reactions of five species are considered CH H20 lt gt CO 3H reaction 1 CO H20 CO He reaction 2 Reaction 2 is the water gas shift WGS reaction The referenced paper Shuyan et al contains the reaction kinetics used in this problem based on the presence of Haldor Topsoe Ni Mg AlzO spinel calatytic particles Because of the demonstrative nature of this problem the details of the catalyst are neglected the catalyst
13. UINT run uses reaction kinetics nor do they use the exact same equilibrium constants though apparently they are very close and that the enthalpy functions fluid properties are different as well Three more cases were compared based on isothermal processes with inlet temperatures being 500 C 800 C and 1000 C Equal mole fractions of methane and steam were used stoichiometric conditions The results are shown below Again the species fraction differences were calculated on the basis of total mass The temperature differences were calculated on the basis of temperature drop from the inlet 500 C 800 C 1000 C Aspen S F diff Aspen S F diff Aspen S F diff CH 0 4342 0 4346 0 04 0 3438 0 3430 0 08 0 2842 0 2828 0 14 H O 0 4020 0 4026 0 06 0 2775 0 2765 0 10 0 2103 0 2087 0 16 CO 0 0006 0 0006 0 00 0 0118 0 0120 0 02 0 0340 0 0345 0 06 CO 0 0323 0 0320 0 02 0 0663 0 0665 0 02 0 0739 0 0741 0 02 H2 0 1309 0 1301 0 08 0 3006 0 3020 0 14 0 3977 0 3999 0 23 Tprod C 367 5 368 3 0 61 477 6 476 9 0 22 531 3 530 3 0 21 Demonstration Use of a CEA derived Equilibrium Fluid It is noteworthy that the Aspen Plus equilibrium calculation yielded results similar to a finite rate approach even at temperatures as low as 370 C This observation means that a variable molecular weight equilibrium fluid may be appropriate at least when the
14. ble to older versions and experienced users the FLOGIC 0 block appears as do itest 1 resol call reform enddo where itest the value iterated in the DO loop refers to the user lump ID from 1 to reso 10 Itest is a global value that is accessible within the user subroutine REFORM as part of the CALL COMMON command in that routine which is inserted as a file subroutine reform call common fstart integer methane water co co2 h2 lump c c reactions 1 and 2 from Simulation of effect of catalytic c particle clustering on methane steam reforming in a c circulating fluidized bed reformer Shuyan et al c Chem Eng Jnl 139 2008 p 136 146 c c H H2 W H20 G CO M CH4 C C02 es c itest is assigned in FLOGIC lump intlmp reactor itest methane intspe reactor m co2 intspe reactor c co intspe reactor g h2 intspe reactor h water intspe reactor w if ppg h2 lump le 0 0 call abnorm reform itest amp User routine REFORM cannot handle zero H2 partial pressure c convert to absolute units if not atemp tl lump abszro apres pl lump patmos c 1 Pa except for KH20 which is unitless KCH4 6 65e 9 EXP 4604 28 atemp Available in Sinaps and FIoCAD Versions 5 2 and later KH2 6 12e 14 EXP 9971 13 atemp KCO 8 23e 10 EXP 8497 71 atemp KH20 1 77e5 EXP 10666 35 atemp DEN 1 0 apres KCH4 PPG methane lump amp KH2 PP
15. ction excess steam SteamX 3 then the SteamX 3 steady state case presented in a prior section could be repeated with the equilibrium fluid approach yielding similar but not completely equivalent results Stoich Methane Water plus a trace H2 CO Extra steam m Se es Das OA De ee De Oa Gk ie OR O O ES OR ees ROS OR E Ng amp SO D amp B HS amp BY T amp GY BB D o set flows R b gt Discretized Reactor el ee 2 el gt ve el wel amp wel wl wl If the molar ratio of steam to methane were to remain at 3 1 a more accurate approach would be to create a new equilibrium fluid E for that scenario using another CEA run and FPROP conversion which is a trivially easy process CH 3H 0 F equivalent reaction SteamX 3 new equilibrium fluid Using an equilibrium fluid approach reduces the number of species tracked from 5 to 3 and also eliminates the extreme sensitivity of the reaction rates to temperature by assuming they re infinitely large The result is a significant increase in computational speed and more robust convergence that is much less sensitive to coarsely guessed initial conditions However the ability to resolve the internal details of the equilibrium fluid are lost as a compromise For example one can no longer plot the fraction of hydrogen since the actual current amount of hydrogen is hidden within the chemical control volume that the equilibrium fluid represents To overcome
16. e the XMDOT for each species in that equation Since XMDOTs have already been updated for reaction 1 this step involves summing into these values which explains why XMDOT for CO XMDOTC was zeroed in the prior step If there were any 3 or 4 reactions these could similarly have been summed into the XMDOT values To avoid any confusion when the number of reactions is large the XMDOTs should be zeroed at the start of the logic block then always summed into rather than replaced so as not to overwrite the effects of reactions calculated earlier in the sequence There are two places where such reaction update logic can be placed 1 HEADER SUBROUTINES user defined subroutines which can then be called from FLOGIC 0 via a DO loop incrementing loop ID Since the ID of each tank will change for each call to the update routine dynamic translation routines e g INTLMP INTSPE will be required to convert the user identifier into the internal array location 2 Network logic logic associated with each network element tanks in this case Expression style indirect referencing can be used in these blocks For example VOL this refers to the volume of the current tank PPGH this refers to the partial pressure fraction of hydrogen species H in the current tank and XMDOTHiHthis refers to the XMDOT of the same species H For the SUBROUTINES approach which is used in the model not because it is recommended but because it is more widely accessi
17. ershadows the illustrative intent of this demonstration problem The chosen scenario focuses on how to incorporate the reaction kinetics into SINDA FLUINT 2 if temperatures below the dew point are included a full two phase description of water should be used instead Indeed such a description http www crtech com properties html was used as part of the validation effort when temperatures as low as 25 C were used as a feed temperature gt http www crtech com EQfluids html Temperatures pressures inlet flows and dimensions may be changed parametrically in the model with a subset of possible parametric settings used for the baseline runs shown in the table below Parameter Register Value Units Comment Name Reactor length length 1 m Arbitrary choice Longer lengths might be considered as needed to bring the outlet conditions closer to the equilibrium condition Reactor hydraulic diameter diam 0 008 m Arbitrary choice Reactor flow area area 4 e 4 m Undefined fins or slit shape is assumed as needed to provide adequate heat transfer area Inlet temperature temp_in 800 C Arbitrary choice but representative of typical applications Wall temperature Assumed 800 C Inlet and wall temperatures are equal to the assumed to be equal but can be inlet independently adjusted if need be Inlet flow rate moles_in 0 03e 3 kmol s Arbitrary choice Inlet mole fractions of CH4 H20 mol_in_m 0 5
18. esses especially species fractions Reactor Model The source of gases is represented by two plena one reactor 1000 representing a stoichiometric mixture of methane and steam and another reactor 1100 representing excess steam that can be added to the reactor The mixture ratio within plenum reactor 1000 is set using registers e g mol_in_w for steam mol_in_m for methane based on mole fractions which are then converted into gas mass fractions XGi for each species i as represented by the register xin_m xin_w xin_h xin_c and xin_g Note that while xin_c and xin_g are both zero no inflowing CO or CO xin_h is nonzero it is set to a very small value An extremely small amount of hydrogen is added simply to avoid the need to deal with the mathematical singularity caused by the presence of the partial pressure of hydrogen in the denominator of the rate equations There are many ways to represent the inlet conditions For example the mass fractions on a single plenum could be set Alternatively N plena could be used for each of the N species involved setting the mass or volumetric flow rate of each species being injected In this case a single SetFlow SINDA FLUINT MFRSET connector is applied from each plenum with the ratio of the flow rates being controlled via the SteamX register SteamX 1 for stoichiometric flow 2 for twice the steam required etc The steady state case named PFR is run at SteamX 1 stoichiometric inlet c
19. illations in the time plots 2 If body forces had been important these variables would not be available for this usage Either other open variables must be sought or extra registers must be declared to hold the memory for each tank s reaction history The experienced user might be wondering why similarly reducing RSSIZF isn t a valid approach for STDSTL solutions avoiding the need for running average damping The reason is that small RSSIZF values would require excessive iterations high LOOPCT unless large values are used initially More importantly the convergence While the approach differs between steady state STDSTL and transient TRANSIENT solutions the cause for this unusual step is the same the extreme temperature dependence of the reaction rates which is to be expected because of the presence of exponential in the Arrhenius rate equation Specifically the XMDOT values are not adjusted implicitly by the code as a function of temperature Rather XMDOT values are assumed constant over each solution step If too large of a step is taken the temperature in the tank will change too much and the assumption of constant reaction rates is invalid the absolute value of the partial derivative of XMDOTi with respect to TL is too high Therefore either the time step must be reduced in anticipation of a significant change in XMDOT the transient approach or the XMDOT value must be damped to prevent binary oscillations the steady
20. is assumed to operate at full activity Shuyan lists formulae for forward reaction rates for these reactions using equilibrium constants as the basis for estimating reverse rates Assuming full catalytic activity the current reaction rate can be calculated as a function of temperature pressure and partial pressures The temperature dependencies for both the reaction rate constants and the equilibrium constants are exponential functions of an Arrhenius form Specifically equations 8 9 11 12 13 and 15 20 Notes on Fluid Properties In SINDA FLUINT each species is assigned a letter identifier Species Symbol Letter ID Methane CH M Water H O W Carbon monoxide gas CO G Hydrogen H2 H Carbon dioxide CO C Water may be a condensable two phase fluid However in this case the temperatures will always be high enough such that the liquid phase will never occur Therefore either a perfect gas 8000 series fluid or a real gas NEVERLIQ 6000 series fluid could have been used Versions of such files are available http www crtech com properties html that were built from the NIST program REFPROP perhaps subsequently simplified to a perfect gas using the SINDA FLUINT PR8000 utility Unfortunately the NIST database does not extend to sufficiently high temperatures for CO CHa and H2 For example the upper temperature limit for CO is only 500K in the current version of REFPROP
21. mperatures are high enough to ensure equilibrium Also the reactor length may need to be increased as well this can be changed independently of the number of segments used to resolve that length thermal solution STDSTL is similar to running a transient solution until every system response is constant It therefore is sensitive to initial conditions as set via the mole fraction registers minit_h minit_g etc which set mass fractions xinit_h xinit_g etc This means that some speed savings can be realized by setting reasonable initial conditions perhaps based on prior runs Otherwise poorly guessed initial conditions invoke the evaluation of a severe yet spurious transient wasting computational resources and requiring more stepNum a register used to set the control constant NLOOPS to converge Normally steady state solutions are so inexpensive that they are often recalculated before each transient case as initial conditions While the speed of the STDSTL solution is good in this case a more detailed perhaps 2D or 3D model might not enjoy the same result Therefore the ability to save the results of a prior steady state case case pfr and reuse them in a future transient case case ofrTransient is demonstrated in this model see RESAVE RESTAR operations in the SINDA FLUINT manual Both cases can be selected in the Sinaps Case Manager or the Thermal Desktop Case Set Manager and executed sequentially If this usage were freque
22. n efficiency based on inflowing methane which was presumed to be the limiting reagent A new register convert set to 0 999 declares that 99 9 of incoming methane will be combined with an equal molar amount of water and replaced by an equal mass of equilibrium fluid E Inflowing methane mass flow is calculated as the product of the mass fraction upstream in junction 1000 xgM1001 and the incoming mass flowrate in path 3 fr3 xmdotM1 xgM1001 fr3 convert xmdotW1 xmdotMl mw_h2o mw_ch4 xmdotEl xmdotM1 xmdotM1 Because excess steam affects the equilibrium point the equilibrium fluid E should only be used to replace a stoichiometric mixture of methane and water Indeed when such a stoichiometric SteamX 1 1 Excess oxidizer e g air can usually be added or subtracted from an equilibrium fluid representing the hot products of combustion This would only be true for a methane reformer in the special case of the addition or subtraction of a chemically inert substance See www crtech com and the SINDA FLUINT User s Manual for further details 11 http www crtech com EQfluids html mixture was tested the resulting temperatures in adiabatic cases matched very well against the Aspen Plus analysis and full reacting flow mixture SINDA FLUINT analysis presented above As a first approximation if the excess steam could be assumed to be independent of the rest of the mixture CH 3H20 lt gt E 2H O equivalent rea
23. ndependent state Stoich Methane Water plus a trace H2 CO Extra steam PPGH SS 2o 2o 2a 2 set flows Discretized Reactor Recalling the presence of excess steam the mole fraction of hydrogen produced is about 56 in the outlet stream Steady state analyses are a key tool for sizing sensitivity studies etc Recall that unlike most SINDA FLUINT models the type of steady state solution used for chemical reactions is not insensitive to guessed initial conditions Therefore either the run time allowed stepNum may have to be enlarged or more accurate initial conditions may need to be guessed registers minit_h minit_c etc or both For parametric sweeps or Solver runs sizing correlation to test etc the guessed initial conditions should reflect the first case to be solved with only modest increases in stepNum to accommodate variations that might be experienced during while solving for varied conditions More significant increase in stepNum may be required for statistical design runs using the Reliability Engineering Module since the variations between samplings are not necessarily gradual the prior steady state answers might not be good initial conditions for the next sampling run to be made Transient Demonstration Event A key feature of SINDA FLUINT reacting flow modeling is the ability to simulate transients including fast transient events such as pressure waves flow instabilities control system ac
24. nt then the two solutions should be combined into a single case to avoid the inefficiencies of the extra preprocess and compile steps For each tank in the system at the start of each solution step namely in FLOGIC 0 the following calculations should be made 1 The rate factors equilibrium K constants and pre exponential k terms should be updated as a function of current temperature TL pressure PL and partial pressures e g PPGH is the partial pressure fraction for species H The temperatures and pressures should be converted into absolute units e g degrees K instead of C which means subtracting ABSZRO from temperatures and PATMOS from pressures For example TLap TLre ABSZRO In the logic blocks the register atemp contains the absolute temperature and apres contains the absolute pressure 2 The molar rate for reaction 1 should be calculated and used to set the XMDOT for each species in that equation using the stoichiometric number noting that XMDOT has units of kg s or lb hr for UID ENG and therefore the molecular weight of each species must be used as a multiplier These molecular weights can be calculated via routines such as VMOLW or VMOLWPT but in this demonstration problem they have been set using registers e g mw_h2o mw_co2 etc If a species is not participating in reaction 1 e g CO in this case its XMDOT should be zeroed 3 The molar rate for reaction 2 should be calculated and used to updat
25. on INTSPE is equivalent to ppgm this in network logic Damping and Time Step Control Dealing with Temperature Sensitivities Inspection of the kinetic rate calculations above reveals that some extra steps were necessary to assure steady state convergence the prior molar reaction rates rate1 and rate2 are stored from the previous iteration in unused lump coordinates CX and CY respectively This approach has a convenient side effect it allows those values to be post processed These prior rates are then used to slow the rate of change of XMDOT values to encourage convergence in steady states according to the register rateLag which varies from an initial value of 0 5 mid range damping via a running average between the current and last value to 1 0 heavy damping by the end of the steady state rateLag 0 5 0 5 loopct stepNum wheres stepNum is the number of pseudo time steps allows used to set NLOOPS and oopct is the current step number For reaction N this damping takes the general format rateNnew 1 0 rateLag rateNnew rateLag rateNog In transients rateLag is set to zero meaning no damping via case dependent registers In other words no damping is required in transients However the default time step error tolerance factor DTSIZF which defaults to 0 1 10 max change per time step in any key parameter such as pressure species fraction etc must be reduced to at most 0 02 2 max change to prevent osc
26. onditions or equal molar flows of methane and steam with zero excess steam flow added from plenum reactor 1100 By default SINDA FLUINT does implicitly reduce reactions for reactants that are present in low concentrations and that vanish during the solution interval as described in the User s Manual In other words XMDOTs can be an implicit function of concentration but they are assumed independent of temperature and pressure during each solution interval Normally they are adjusted in a stair step fashion between solution intervals according to calculations in user logic A 10 segment Sinaps or FloCAD Pipe SINDA FLUINT HX macro plus wall model is used to represent the reactor While including the details of the heat exchange structural thermal model is a strength of the C amp R tool suite to avoid distracting from the intent of this demonstration problem an infinite source of energy at 800 C is assumed The nodes in the Pipe are therefore chosen to be constant temperature boundary nodes The choice of 10 segments can be adjusted by changing both the integer register resol plus editing the Pipe macro Higher resolutions at least reso 20 are needed to capture the strong gradients at the inlet and to guarantee that equilibrium is achieved at the exit However for demonstration purposes the spatial resolution is left intentionally low The Sinaps diagram for the reactor is show below Stoich Methane Water Outlet sets pressure
27. return end fstop The equivalent to the above using the network logic approach is to place the following in the FLOGIC O form for all tanks which can be edited simultaneously particle clustering reactions 1 and 2 from Simulation of effect of catalytic on methane steam reforming ina circulating fluidiz d bed reformer Shuyan et al Chem Eng Jnl 139 2008 p 136 146 Tra A a QANCA H H2 W H20 G CO M CH4 C CO2 if ppgh this le 0 0 call abnorm reform this amp User logic cannot handle zero H2 partial pressure c convert to absolute atemp tl thi apres pl thi units if not s abszro s patmos c 1 Pa except for KH20 which is unitless 9 EXP 4604 28 atemp 14 EXP 9971 13 atemp 10 EXP 8497 71 atemp KCH4 6 65e KH2 6 12e KCO 8 23e KH20 1 77e5 DEN 1 0 EXP 10666 35 atemp apres KCH4 PPGM this KH2 PPGH this KCO PPGG this amp KH20 PPGW this PPGH this c reaction 1 c mol sqrt Pa kg s klicl 8 336e17 EXP 28879 atemp c Pa 2 Kucl 10266 76e6 EXP 26830 atemp 30 11 rxnl klcl ppgm this ppgw this ppgh this 2 5 amp apres 2 ppgg this sqrt ppgh this Kucl amp sqrt apres DEN 2 ratel rxnl dl this vol this ratel 1 0 rateLag ratel rateLag cx this xmdotm this ratel mw_ch4 xmdotw this ratel mw_h2o xmdotg this ratel mw_co xmdoth this 3 0 ratel mw_h2 xmdotc this 0
28. roduced one that does not contribute to the gas pressure Even though there are no solid species per se in SINDA FLUINT a 9000 series nonvolatile liquid is an adequate substitute with fake viscosity and surface tension values as needed to comply with input requirements By default this fluid will be assumed to mix homogeneously with the remaining species Three more chemical reactions would need to be included CH lt gt C 2H reaction 3 2CO C CO reaction 4 CO H lt gt C H2O reaction 5 Equations 25 30 of the referenced paper Shuyan et al provide the relevant equilibrium K constants and pre exponential k terms for these reactions Acknowledgments The assistance of John Persichetti of Colorado School of Mines in developing and validating this model is gratefully noted
29. tions and valve dynamics As a demonstration of these capabilities the steady state solution described in the last section will be used as the initial condition for an arbitrary event the reduction of steam injection to stoichiometric conditions a threefold decrease in steam feed at time zero with an approximately two fold reduction in overall flow rate Normally a transient case is run simply by adding a call to the TRANSIENT solution routine following the call to the steady state solution STDSTL within OPERATIONS In the sample models associated with this document the steady state and transient analyses are performed as two separate cases pfr and pfrTransient respectively The pfrTransient case starts by reading back the initial conditions left for it by the pfr case which must have been executed beforehand If some dimension or boundary condition is changed that affects both cases they should both be selected and rerun together The plot below shows the transient temperature response of the reactor to a step reduction in steam injection As the flow rate diminishes the temperatures at the exit e g TL10 the temperature of lump 10 rise reflecting their temporary stagnation next to a hot wall Near the inlet TL1 the temperature actually goes down before rising since there is less steam to cool from 800 C but the endothermic reaction continues at about the same rate As a new steady condition is established the net change is
30. tions based on the minimization of Gibb s free energy In addition the energy inputs needed to sustain an isothermal process can be calculated as can the energy required when the feed temperature is substantially colder than the product temperature Finally the temperature drop experienced by hot steam and methane injected into an adiabatic reactor can also be calculated It is important to remember that all of the Aspen Plus calculations assumed equilibrium conditions to exist whereas the SINDA FLUINT predictions were made by simulating finite rate reactions as a process In other words to be able to predict the heat added to a stoichiometric stream injected at 25 C and heated to say 1200 C the reactor walls were set to 1200 C and sufficient reactor length was added as needed to provide the heat transfer required to accomplish this task The exit state was then compared with Aspen Plus predictions and the heat added to the stream via heat transfer was tallied to generate a total net power Compared with the models presented above and included with this sample up to three differences were made in the variation of the demonstration model that was used to generate comparison results 1 The length was increased up to 40m 2 The resolution was increased from 10 segments to 20 3 A two phase description of water REFPROP derived f6070_water inc was substituted when 25 C inlet conditions were used such that the fact that water is
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